a listmania: essentials of undergraduate math for aspiring applied math students
Since I’ve been using amazon so much lately, I decided I might as well take the plunge and use all its features. Just finished the first revision of my first listmania. Comments or suggestions for additions (keeping in mind the orthogonality condition)? I can’t think of any good ODE books.
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Nice list. Would you be extending it to cover areas like algebra and differential geometry/topology? For ODEs, my own favourites are Arnold and Hirsch and Smale.
Comment by AnonEcon — 3/30/2007 @ 8:12 pm
Because it’s for applied math people, I don’t think algebra is too important, but differential geometry is definitely something I overlooked. Any suggestions?
Jeez, did you read those when you were an undergrad? I’m impressed. I consider pretty much all qualititative ODE material to be graduate level (maybe just because I find it confusing).
I was thinking of more of a guide to analytic solution techniques like green’s functions, power series expansions, variation of parameters, etc. Any recommendations?
Comment by Alex — 3/31/2007 @ 10:38 pm
I found Munkres’Analysis on Manifolds very user-friendly.
I’m still reading Arnold and Hirsch-Smale. But I find them more interesting and intuitive than the traditional books. And the prerequisites are about the same: basic analysis and linear algebra. In fact Hirsch-Smale lessens the load even further by developing lot of the linear algebra itself and replacing some of the analysis by hand-waving (at one point substituting the Jordan curve theorem by a neat diagram).
Among the traditional ODE books which I have seen, I really liked Simmons.
Comment by AnonEcon — 3/31/2007 @ 11:39 pm
about odes, I prefer Simmons (perhaps the best for applied people), followed by the Hirsch-Smale and the classical Coddington.
And do Carmo is a very good book for differential geometry.
Comment by JuanPablo — 4/3/2007 @ 7:26 pm